Alyson Footer is live-tweeting from the Arnsberg press conference, and has some quotes (joined together for your reading enjoyment).
"He developed a great rapport with each and every one of his pitchers. This is not about his ability to coach or communicate with his players. He got very high grades on both." Wade cites philosophical differences, declines to elaborate on specifics.
"Arnie has brought an awful lot to this ballclub. He's done a good job. To have to do something like this is kind of tough but at the same time, we're trying to create an atmosphere to accomplish things and make these guys successful." Mills also declined to get into specifics. "He's done a great job working with the pitchers and that's where it needs to stay."
So there was a whole lot of press conference where absolutely nothing was said. Not that you would expect such a key part of the coaching staff to get lambasted within six hours of being let go. This could go one of two ways:
(1) Potential hire-ees could appreciate not airing dirty laundry. Or
(2) Higher-profile replacements could be wary of taking a job where you can get canned for bad pitchers playing poorly.